Hilbert Series of Fiber Cones of Ideals with Almost Minimal Mixed Multiplicity

Abstract

dedicated to william heinzer on the occasion of his 60th birthday Let R m be a Cohen-Macaulay local ring and let I be an m-primary ideal. We introduce ideals of almost minimal mixed multiplicity which are analogues of ideals studied by J. Sally [Compositio Math. 40 (1980), 167-175]. The main theorem describes the Hilbert series of fiber cones of these ideals.  2002 Elsevier Science (USA)

The Hilbert Coefficients of the Fiber Cone and the a-Invariant of the Associated Graded Ring

“…One can verify that the Hilbert-Series of F (K) is Be giving the next example we make the following: Remark 5. 8. If A satisfies the condition of the theorem then as a(I) < 0 we get by 2.5 that red J [n] (I n ) = 2 for all n ≫ 0.…”

Depth of fiber cones of ideals with almost minimal mixed multiplicity

“…We apply induction on d. Let d = 2. Since I has almost minimal mixed multiplicity, λ( mI n a 1 mI n−1 +a 2 I n ) 1 for all n 1 by Lemma 2.2 of [6]. Let " " denote the image modulo (a 1 ).…”

On the depth of fiber cones of stretched m-primary ideals

“…We say that I has minimal mixed multiplicity if e d−1 (m|I) = µ(I)−d+1 and I has almost minimal mixed multiplicity if e d−1 (m|I) = µ(I)−d+2. In [6] and [7], the Cohen-Macaulay property of fiber cones of ideals with minimal and almost minimal mixed multiplicities was studied. J. Chuai, in [3], proved that for an m-primary ideal I in a Cohen-Macaulay local ring (R, m), e(I) ≥ µ(I) − d + ℓ(R/I).…”